Food in a hostel is sufficient for 50 students for 45 days (steady consumption). If 75 students share the same stock, for how many days will it last?

Introduction:
This is a direct man-days (or student-days) proportionality problem. For fixed total food, the product of consumers and days stays constant. Increasing the number of consumers reduces the duration in inverse proportion.

Given Data / Assumptions:

• Total food equals 50 students * 45 days of consumption.
• New consumer count = 75 students.
• Consumption per student per day remains unchanged.

Concept / Approach:
Let D be the new duration. Since student-days are constant, 50 * 45 = 75 * D. Solve for D using unitary-method proportionality (inverse relation of days with students for fixed stock).

Step-by-Step Solution:

Verification / Alternative check:
Ratio approach: days scale by 50/75 = 2/3. Apply to 45 days → 45 * (2/3) = 30 days, confirming the result.

Why Other Options Are Wrong:
25, 28, 36, or 40 days do not preserve the student-day total 2250 under unchanged per-head consumption.

Common Pitfalls:
Using direct proportion instead of inverse (days decrease when students increase for fixed stock). Keep the product students * days constant.

Final Answer:
30 days